Definition 71.18.1. With Z \subset B and f : X \to B as above.
Given a quasi-coherent \mathcal{O}_ X-module \mathcal{F} the strict transform of \mathcal{F} with respect to the blowup of B in Z is the quotient \mathcal{F}' of \text{pr}_ X^*\mathcal{F} by the submodule of sections supported on |\text{pr}_{B'}^{-1}E|.
The strict transform of X is the closed subspace X' \subset X \times _ B B' cut out by the quasi-coherent ideal of sections of \mathcal{O}_{X \times _ B B'} supported on |\text{pr}_{B'}^{-1}E|.
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